Imaginary experiment on gravity.

[satipatana]

I am not good at maths but very passionate about physics (I know is sad). I am trying to imagine how strong (or weak) the force of gravity is, so I have this imaginary experiment:

[BWe have to stones of, let's say, one kilo each floating in a void, separated by let's say one meter. In absence of any other influence would gravity be strong enough to make them move towards each other. If so, would the movement be perceptible for a human being (a massless human being!).

As you can see is not about the numbers, it is mor an effort to visualize. Thanks everybody this forum is fantastic!

 

[Bandersnatch]

Hi satipatana, welcome to PF!

Without doing any calculations, try applying Newton's laws of motion(1st and 2nd) to your setup(no other forces but gravity). Tell us what do you think will happen.

Also, try to tell us why do you think everyday objects often don't move even though there's a force applied to them(like pushing a heavy stone).

 

[satipatana]

Thanks for the quick reply!

I am afraid I am not able to do the simplest calculations and even if I did I would have problems to understand the magnitudes, that is why I asked if the movement (if there is one) could be noticed by a human being.

Trying to answer your question I guess everyday objects don't move until the force applied is bigger than the drag of the medium, that is why I imagine the two stones in a void.

 

[Bandersnatch]

O.k., so if there's no drag in the void, what will happen to the stones?

 

[satipatana]

They would move towards each other. That is what I think (eventhough I would not be surprise if you told me that the answer is no, my common sense seems not to be very useful sometimes). But what I am very curious about is: Would it be a movement that I could see with naked eyes?

 

[Bandersnatch]

"see movement with naked eyes" is a very vague statement. After all, seeing movement is not the same as resolving miniature objects.
If something is so small that it's below your eyes' resolution, you won't be able to see it in principle.
But with movement it's just a matter of comparing positions at two distinct times. Wait long enough and you'll see the displacement. Whether you will or won't be able to see it is just a matter of patience.

In your example the two stones would begin to accelerate towards each other with something like 0.0000007 mm/s^2(that's about the width of an atom per second). Even if you kept pushing the other stone away to make sure it always stays 1 metre away, the first stone would be moving at 7mm/s after a hundred million seconds(a bit over three years).
Of course, as the stones get closer, they would attract each other more, and accelerate more, so in reality you wouldn't need to wait that long to see them move.

The bottom line here is: you wouldn't be able to see the movement at first, but wait just eneough time, and you will.

 

[satipatana]

Your answer matches exactly my question. Actually it gives me much more to think about. I never thought that even if I keep pushing one stone to keep the distance the other would still accelerate.

Thanks a lot for your patience!

 

[satipatana]

Now I got it. Keeping the distance by pushing stone A means the force applied will be always the same and the result of that is not that stone B will keep on moving t the same speed (as I first thought) but that it will
accelerate.

For you must be obvious but I must be honest: I has taken me a big deal of thinking to accept this! My common sense was totally attached to the wrong view.

Thanks again, this is a fantastic forum!

 

[Bandersnatch]

Look up Newton's Laws of Motion on the net! Wikipedia, as always, is a good start. You don't really need maths to "get them", and they'll let you properly rewire your common sense. As it is, you do seem to have the right idea, it's just that you can't always decide when to trust your gut feeling.

The Laws are three simple statements, that are always true. Read what they say, and try applying them to everyday situations and thought experiments.

 

[satipatana]

Your analysis of my situation is in fact very accurate. I like the expression you use "rewire your common sense". I will follow your advice.

Thanks a million, your words are very encouraging.